Final answer:
When vectors →A and →B are orthogonal (perpendicular), the component of →B along →A and the component of →A along →B are both zero.
Step-by-step explanation:
When two vectors →A and →B are described as orthogonal, it implies that they are perpendicular to each other. In this case, the angle between →A and →B is 90 degrees. As a result, the component of →B along the direction of →A is zero, and vice versa, the component of →A along the direction of →B is also zero. This is because the orthogonal projection of one vector onto another that is perpendicular yields a projection length of zero.
Considering a scenario where you project →B onto →A, it's like casting a shadow of →B along the direction of →A. However, because they are perpendicular, the 'shadow' or projection doesn't actually fall on →A; it's like the sun is directly overhead, so the shadow is non-existent. Hence the projection, or the component of →B along →A, is zero.
The same logic applies when considering the component of →A along the direction of →B. There is no length of →A that lies along →B, because of their perpendicular orientation to one another.
Therefore, the correct answer is: a) →B component along →A: 0, →A component along →B: 0.